Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Non-stationary Time Series

Here we propose a method, based on detrended covariance which we call detrended cross-correlation analysis (DXA), to investigate power-law cross-correlations between different simultaneously-recorded time series in the presence of non-stationarity. We illustrate the method by selected examples from physics, physiology, and finance.Comment: 11 pages, 7 picture

Effect of strong opinions on the dynamics of the majority-vote model

We study how the presence of individuals with strong opinions affects a square lattice majority-vote model with noise. In a square lattice network we perform Monte-Carlo simulations and replace regular actors σ with strong actors μ in a random distribution. We find that the value of the critical noise parameter q c is a decreasing function of the concentration r of strong actors in the social interaction network. We calculate the critical exponents β/ν, γ/ν, and 1/ν and find that the presence of strong actors does not change the Ising universality class of the isotropic majority-vote model.The authors acknowledge financial support from UPE (PFA2016, PIAEXT2016) and the funding agencies FACEPE (APQ-0565-1.05/14), CAPES and CNPq. The Boston University Center for Polymer Studies is supported by NSF Grants PHY-1505000, CMMI-1125290, and CHE-1213217, by DTRA Grant HDTRA1-14-1-0017, and by DOE Contract DE-AC07-05Id14517. (UPE (PFA, PIAEXT); APQ-0565-1.05/14 - FACEPE; CAPES; CNPq; PHY-1505000 - NSF; CMMI-1125290 - NSF; CHE-1213217 - NSF; HDTRA1-14-1-0017 - DTRA; DE-AC07-05Id14517 - DOE)Published versio

Analysis and evaluation of the entropy indices of a static network structure

Although degree distribution entropy (DDE), SD structure entropy (SDSE), Wu structure entropy (WSE) and FB structure entropy (FBSE) are four static network structure entropy indices widely used to quantify the heterogeneity of a complex network, previous studies have paid little attention to their differing abilities to describe network structure. We calculate these four structure entropies for four benchmark networks and compare the results by measuring the ability of each index to characterize network heterogeneity. We find that SDSE and FBSE more accurately characterize network heterogeneity than WSE and DDE. We also find that existing benchmark networks fail to distinguish SDSE and FBSE because they cannot discriminate local and global network heterogeneity. We solve this problem by proposing an evolving caveman network that reveals the differences between structure entropy indices by comparing the sensitivities during the network evolutionary process. Mathematical analysis and computational simulation both indicate that FBSE describes the global topology variation in the evolutionary process of a caveman network, and that the other three structure entropy indices reflect only local network heterogeneity. Our study offers an expansive view of the structural complexity of networks and expands our understanding of complex network behavior.The authors would like to thank the financial support of the National Natural Science Foundation of China (71501153), Natural Science Foundation of Shaanxi Province of China (2016JQ6072), and the Foundation of China Scholarship Council (201506965039, 201606965057). (71501153 - National Natural Science Foundation of China; 2016JQ6072 - Natural Science Foundation of Shaanxi Province of China; 201506965039 - Foundation of China Scholarship Council; 201606965057 - Foundation of China Scholarship Council)Published versio